During the development of the unique pipette tip described in U.S. patent application Ser. No. 09/188,030, filed Nov. 6, 1998 now U.S. Pat. No. 6,197,259 and entitled "Easy Eject Pipette Tip" and the development of the novel pipette tip and tip mounting shaft combination described in U.S. patent application Ser. No. 09/188,031, filed Nov. 6, 1998 now U.S. Pat. No. 6,168,761 and entitled "Pipette With Improved Pipette Tip and Mounting Shaft", both applications being incorporated herein by this reference, a special pipette tip and mounting shaft combination was discovered which provides for easier tip mounting, improved lateral tip stability and easier tip ejection than standard commercially available pipette tip and tip/shaft combinations. A brief description of the newly discovered pipette tip and mounting shaft combination is as follows.